Finite Depth and Tank Wall Effects Upon First and Second-Order Forces

1991 ◽  
Vol 113 (4) ◽  
pp. 297-305 ◽  
Author(s):  
G. E. Hearn ◽  
S. Y. Liou
Keyword(s):  
Low Frequency ◽  
Open Water ◽  
Finite Depth ◽  
Second Order ◽  
Confined Water ◽  
Rankine Source ◽  
Method Of Solution ◽  
Direct Pressure ◽  
Expansion Matching ◽  
Matching Techniques

This paper presents a hybrid method of solution of the radiation and diffraction fluid-structure interaction problems based upon Rankine source distributions and eigenfunction expansion matching techniques. Using direct pressure integration of the first-order solutions, the second-order drift forces are calculated in “open” water and “confined” water situations with and without forward speed effects included. The method has been developed to provide an alternative way of calculating low-frequency damping coefficients.

Second Order Loads on LNG Terminals in Multi-Directional Sea in Water of Finite Depth

2007 ◽  
Author(s):  
Fla´via Rezende ◽  
Xin Li ◽  
Xiao-Bo Chen
Keyword(s):  
Near Field ◽  
Low Frequency ◽  
Finite Depth ◽  
Accurate Method ◽  
Second Order ◽  
Wave Loading ◽  
Storage Tanks ◽  
Offshore Area ◽  
Directional Waves ◽  
Poor Convergence

Large LNG terminals are designed to be installed in an offshore area approximate to harbors where the water is of finite depth and waves are multi-directional. The terminal can be of a barge type LNG/FRSU including accommodations, gas preconditioning and liquefied plant, a number of storage tanks and offloading facilities. It serves also as a support to moor a LNG carrier during offloading operations. In the design of such mooring system of LNG/FRSU and LNG carriers in a zone of shallow water, one key issue is the accurate simulation of low-frequency motions of the system to which the second-order wave loading is well known as the main source of excitation. The computation of second-order wave loading in multi-directional waves of finite waterdepth is considered here. New formulations obtained recently in [1] for the computation of second-order loads in mono-directional waves are extended to the case of multi-directional waves. Both the classical near-field formulation and the new middle-field formulation developed in [1] are used and numerical results are compared. Unlike the usual near-field formulation giving results of second-order loads with poor convergence, the middle-field formulation provides an accurate method for the computation of vertical components.

scholarly journals A Low-Power Opamp-Less Second-Order Delta-Sigma Modulator for Bioelectrical Signals in 0.18 µm CMOS

Sensors ◽  
2021 ◽  
Vol 21 (19) ◽  
pp. 6456
Author(s):  
Fernando Cardes ◽  
Nikhita Baladari ◽  
Jihyun Lee ◽  
Andreas Hierlemann
Keyword(s):  
Low Power ◽  
Low Frequency ◽  
Cmos Technology ◽  
Low Noise ◽  
Second Order ◽  
Frequency Noise ◽  
Voltage Controlled Oscillator ◽  
Noise Shaping ◽  
Delta Sigma Modulator ◽  
Delta Sigma

This article reports on a compact and low-power CMOS readout circuit for bioelectrical signals based on a second-order delta-sigma modulator. The converter uses a voltage-controlled, oscillator-based quantizer, achieving second-order noise shaping with a single opamp-less integrator and minimal analog circuitry. A prototype has been implemented using 0.18 μm CMOS technology and includes two different variants of the same modulator topology. The main modulator has been optimized for low-noise, neural-action-potential detection in the 300 Hz–6 kHz band, with an input-referred noise of 5.0 μVrms, and occupies an area of 0.0045 mm2. An alternative configuration features a larger input stage to reduce low-frequency noise, achieving 8.7 μVrms in the 1 Hz–10 kHz band, and occupies an area of 0.006 mm2. The modulator is powered at 1.8 V with an estimated power consumption of 3.5 μW.

A theory for Langmuir solitons

1982 ◽  
Vol 27 (1) ◽  
pp. 95-120 ◽  
Author(s):  
N. Nagesha Rao ◽  
Ram K. Varma
Keyword(s):  
Mach Number ◽  
A Priori ◽  
Low Frequency ◽  
Analytic Solutions ◽  
Smooth Transition ◽  
Langmuir Waves ◽  
Method Of Solution ◽  
Mach Numbers ◽  
Ion Waves ◽  
Langmuir Solitons

A systematic and self-consistent analysis of the problem of Langmuir solitons in the entire range of Mach numbers (0 < M < 1) has been presented. A coupled set of nonlinear equations for the amplitude of the modulated, high-frequency Langmuir waves and the associated low-frequency ion waves is derived without using the charge neutrality condition or any a priori ordering schemes. A technique has been developed for obtaining analytic solutions of these equations where any arbitrary degree of ion nonlinearity consistent with the nonlinearity retained in the Langmuir field can be taken into account self-consistently. A class of solutions with non-zero Langmuir field intensity at the centre (ξ = 0) are found for intermediate values of the Mach number. Using these solutions, a smooth transition from single-hump solitons to the double-hump solitons with respect to the Mach number has been established through the definitions of critical and cut-off Mach numbers. Further, under appropriate limiting conditions, various solutions discussed by other authors are obtained. Sagdeev potential analyses of the solutions for the Langmuir field as well as the ion field are carried out. These analyses confirm the transition from single-hump solitons to the double-hump solitons with respect to the Mach number. The existence of many-hump solitons for higher-order nonlinearities in the low-frequency ion wave potential has been conjectured. The method of solution developed here can be applied to similar equations in other fields.

scholarly journals Semicircular Patch-Embedded Vivaldi Antenna for Miniaturized UWB Radar Sensors

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 5988
Author(s):  
Jungwoo Seo ◽  
Jae Hee Kim ◽  
Jungsuek Oh
Keyword(s):  
Electric Fields ◽  
Impedance Matching ◽  
Low Frequency ◽  
Electrical Fields ◽  
Radar Sensors ◽  
Gain Enhancement ◽  
Uwb Radar ◽  
Vivaldi Antenna ◽  
Matching Techniques ◽  
Good Agreement

A microstrip-to-slot line-fed miniaturized Vivaldi antenna using semicircular patch embedment is proposed in this study. The conventional Vivaldi antenna has ultrawide bandwidth, but suffers from low gain in the low-frequency band. The proposed antenna topology incorporates the embedment of semicircular patch elements into the side edge of the antenna. This enables the phases of electric fields at both ends of the antenna to be out of phase. Since the distance between the two ends are λL/2 where λL is the wavelength at a low operating frequency, this antenna topology can achieve the constructive addition of electrical fields at the radiating end, leading to gain enhancement at the chosen low frequency. In comparison with the conventional Vivaldi antenna, the proposed antenna has a wider bandwidth from 2.84 to 9.83 GHz. Moreover, the simulated result shows a gain enhancement of 5 dB at low frequency. This cannot be realized by the conventional low-band impedance matching techniques only relying on slotted topologies. The measured results of this proposed antenna with a size of 45 × 40 × 0.8 mm3 are in good agreement with the simulated results.

scholarly journals Inversion of low-frequency subsurface data in a finite-depth ocean

1994 ◽  
Vol 7 (1) ◽  
pp. 11-14
Author(s):  
L. Couchman ◽  
D.N. Ghosh Roy ◽  
A.G. Ramm
Keyword(s):  
Low Frequency ◽  
Finite Depth

scholarly journals On the dynamic homogenization of periodic media: Willis’ approach versus two-scale paradigm

2018 ◽  
Vol 474 (2213) ◽  
pp. 20170638 ◽  
Author(s):  
Shixu Meng ◽  
Bojan B. Guzina
Keyword(s):  
Low Frequency ◽  
Second Order ◽  
The Body ◽  
Clear Understanding ◽  
Periodic Media ◽  
Physical Sciences ◽  
Static Approximation ◽  
Long Wavelength ◽  
Modulation Factor ◽  
Effective Impedance

When considering an effective, i.e. homogenized description of waves in periodic media that transcends the usual quasi-static approximation, there are generally two schools of thought: (i) the two-scale approach that is prevalent in mathematics and (ii) the Willis’ homogenization framework that has been gaining popularity in engineering and physical sciences. Notwithstanding a mounting body of literature on the two competing paradigms, a clear understanding of their relationship is still lacking. In this study, we deploy an effective impedance of the scalar wave equation as a lens for comparison and establish a low-frequency, long-wavelength dispersive expansion of the Willis’ effective model, including terms up to the second order. Despite the intuitive expectation that such obtained effective impedance coincides with its two-scale counterpart, we find that the two descriptions differ by a modulation factor which is, up to the second order, expressible as a polynomial in frequency and wavenumber. We track down this inconsistency to the fact that the two-scale expansion is commonly restricted to the free-wave solutions and thus fails to account for the body source term which, as it turns out, must also be homogenized—by the reciprocal of the featured modulation factor. In the analysis, we also (i) reformulate for generality the Willis’ effective description in terms of the eigenfunction approach, and (ii) obtain the corresponding modulation factor for dipole body sources, which may be relevant to some recent efforts to manipulate waves in metamaterials.

Transformations between second order linear differential equations and a reinterpretation of recurrence relations between Bessel functions with algebraic coefficients

1977 ◽  
Vol 79 (1-2) ◽  
pp. 87-105 ◽  
Author(s):  
John Heading
Keyword(s):  
Differential Equations ◽  
Recurrence Relations ◽  
Bessel Functions ◽  
Asymptotic Methods ◽  
Second Order ◽  
Schwarzschild Black Hole ◽  
Matrix Methods ◽  
Large Numbers ◽  
Method Of Solution ◽  
Linear Differential

SynopsisA scheme devised by Chandrasekhar for investigating the transformations between various differential equations of the second order governing perturbations of the Schwarzschild black hole demands further investigation. The transformation between two differential equations in normal form is considered, and a wide survey of the properties of the transformation is given. It is shown how Chandrasekhar's equations fit into the scheme, after which some examples with particular properties are considered. A detailed investigation of Bessel's equation is undertaken using various devices, in particular by employing asymptotic methods for products of Bessel functions, and employing matrix methods for dealing with large numbers of matrix equations which necessitates an interesting method of solution, the results being reinterpretations of the standard recurrence relations for Bessel functions.

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